Width of the central bright band in the diffraction pattern of a single slit

The widths and separations of the bright bands on the screen behind the slit depend on the distance between the slit and the screen. For this reason, the distribution of light intensity on a

diffracted light

Figure 8.24 Calculating the position of the first minimum.

screen behind the slit is usually described not as a function of position on the screen but in terms of angular position (the angle at which light leaves the slit).

The angular positions of the minima on either side of the central bright band can be calculated by mentally dividing the slit into two and calculating the angle at which wavelets from pairs of points such as A and B in Figure 8.24 interfere destructively.

The path difference between the rays from points A and B is

Triangle ADB is right angled:

The rays are completely out of phase if

The corresponding value of d is given by sin 0 = = —

For small values of 0,

0 0

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